Lyon have turned down a bid worth ?31million from West Ham for Alexandre Lacazette, club owner Jean-Michel Aulas has said.
Aulas told French newspaper Le Progres the offer from the Hammers was the biggest so far tabled for the striker.
The 24-year-old France international has been a prolific scorer for Lyon in the French league for three seasons.
West Ham will move from Upton Park to London's Olympic Stadium for next season.
Aulas was asked if Lyon had received offers for Lacazette, and said: "Yes. Many, the most important being that of West Ham for 40 million euros (?31million) which we've refused. I want to keep him but I'm not certain because it's he who will decide in the end."
Aulas detailed Lyon's position, telling the newspaper: "To have a sale, you need all three parties to be in agreement. We hope to keep him. Now, if there are offers...
"Last season I expect Monaco wanted to keep (Anthony) Martial (who moved to Manchester United).
"What I don't want is that, by August 28, when we've qualified for the Champions League, we find ourselves in the same situation.
"If there's an offer he can't refuse, he'll come to see me."